2. Let o and b be real numbers satisfying 1 1 a 6. Which of the following is incorett?

4. Jenny and Mary received identica.l fruit baskets, ea-ch containing 3 apphs, 4 oranges and 2 bananas. Assuming that both Jenny and Mary randomly picked a liuit fiom their own basket, wha.t is the probability that they both picked a,r apple?

(A) ; (B) ; (c) ; 1l) ; (E) None or the above

5. A cylinder has base radius r and height ?r. If a sphere has the same surface arca as the cylinder, find the ratio of the volume of the tylinder to ihe votume of the sphere. 1dt fA, "4J2r32 rB, ' rc, a ,o, "t

Let ABC D be a rcctangular sheet of paper with ,48 = 6 and BC : 8. We can fold the paper aloag the crease line t-P so that point C coincides with point ,4. Find the lengih of the resulting line segment ,4I -

AED

(A) 25 ,*, ]! l(-27 )t (D)'7 (E) None of the abowe 42 7l Given tlree consecuti\ positi\ iateg;rs, whlch of the follorring is a pbssible ralue for the ditrrence of iLe squares oI Lihe larycsl :r,nd the smallesi of ihese three iriegers?

e1 (B) g2 (c)' e3 (D) e4 (E) e5

lA) 8. You have 30 rods of length 5, 30 mds of length 17 ard 30 .ods of tength 19. Usiag each .od at most once, how ma.ny non-congruent tria.ngles can you form?

(A) 6 (B) 7 (c) 8 iD) e (E) 10

9. Let a arld 6 be positive integels. If the highest co]I1mon facror of a and 6is 6 and the lowst common multiple of a and b is 233455, how many possible values a.re there for a?

(A) i (B) -1 (c)

12. Find the mrmber of multiptes of 7 ir the sequence 80,81,82,...,2016,2017.

13. A list of six positi.!.e intege$ has a unique mode of 4, median of 6 and mea.n of 8. Find the lalgest possible inteser in the list.

14. In the diagram, ,4F is a dianeter of the ctucle aJld ,4BCD is a square with points B and C on -4F and poinis A and D on the circle. If AB = 17.y/5 find the lensth of rF.

15. Find tbe remainder when

2017r + 20772 +... + 2or12or7

is diwided by 9.16. Assume that

\r lz)'!ai 1r,211016 lr i2,2ooo o,n1t2o- t o.0ro."2016 - ax+aa.

F: d rhe valuF ol thF following Fxprpssion:

(ao - or) + (az a3) + (aa a5) +. + (ozon ozon).

17. l' .r - ,"/2D17 l, frnd In" vdluc of

x3 Q+ \O,OlTx2 + (1+ 2\4]017)r - \r2U7.

18. Let ABC be a t a.ngle, D be a point on Ad such that .4D = DC and E be a point on BC such that B-U : 2rd. Let I. be the intersection of BD and AE. If the area of tdangle ,4BC is 100, find the area of triafigle ADi'.

19. Find the laxgest integer from 1 to 100 which has exactly 3 positive integer divisols. For example, the only positive divisom of 4 arc 1, 2 and 4.

r 20 7V1+20r6Vr- 20rs,v/r 20rav4 -20R . 20 .

If one of the integers is rcmorred from the first N consecutir inteeers 1,2,3, .. .. N, the rFsu riDg d\eragF ot thp rpmanins ir rpse-s is .'^O n. ?.34. Amongst the fractions 723 174 175' 1,75' !75" 175', there a.re some which can be rcduced to a fraction \vith a smaller denominator such as tfu : *1, and there are some that cannot be rcduced further like r75!. Find the sum of alt the ftactions vhich cannot be reduced further.

35- The number of seashells collected by 13 boys and n girls is n2 + 10n 18. If each child collects eiactly the same number of seashells, determine the !?lue of n.